The actress, 17, and the son of David and Victoria Beckham, 15, have been spotted enjoying several spin class dates at Soul Cycle in Brentwood, a source tells PEOPLE.

"They cycle next to each other and are very cute. Always look to be cheering each other on with smiles. They also both seem very competitive, but in a fun way," the source says.

"Brooklyn is always chaperoned by one of his parents. But both David and Victoria must be okay with Chloë, because they will chat briefly with her and then leave them alone."

A separate source says that during the class, Brooklyn leaves his famously athletic father in the dust.

"He comes in with his parents – one or the other. He's adorable. You usually see him come in with his dad, who is obviously gorgeous, and all the women in the class just stare," the source reveals.

"It's not that unusual for Brentwood moms to come in with an older kid, but most of the time, the parents are better at the class than their children are – it's an intensive exercise class for adults, and the adults are really into it. You'd think David would be awesome at it, but in fact, Brooklyn just crushes it. He's incredibly talented and athletic and runs circles around the rest of us."

Adds the source: "[Brooklyn] can do all these amazing moves. He's a natural athlete. You don't know what he's going to do next, but you can tell he's got that Beckham gene."